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TRS Stand 20472 pair #381710565
details
property
value
status
complete
benchmark
downfrom.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.174278974533 seconds
cpu usage
0.171203108
max memory
7135232.0
stage attributes
key
value
output-size
1611
starexec-result
MAYBE
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o Cons : [o * o] --> o cond : [o * o] --> o downfrom : [o] --> o f : [o] --> o isList : [o] --> o nil : [] --> o s : [o] --> o tt : [] --> o isList(nil) => tt isList(Cons(X, Y)) => isList(Y) downfrom(0) => nil downfrom(s(X)) => Cons(s(X), downfrom(X)) f(X) => cond(isList(downfrom(X)), s(X)) cond(tt, X) => f(X) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> va Cons : [va * sa] --> sa cond : [ta * va] --> cb downfrom : [va] --> sa f : [va] --> cb isList : [sa] --> ta nil : [] --> sa s : [va] --> va tt : [] --> ta +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995.
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